The widespread problem could be arrested if not solved, by placing the disease process in remission. And that is done by drying out and followed by complete abstinence. It's a choice they could make. Or not.
There was also a huge input from the religious sector (that would not be possible in today's Sweden, all the religious people having emigrated to other countries).
We aren't talking about a "normal" experience when we get to life on the reservations. If I were the tribal elders I'd start with a peaceful attempt to shut down the access to liquor. Sounds like that's what they are doing.
Oh, and undo the land use patterns established by Teddy Roosevelt. Get that done right away.